CN113031436A - Mobile robot model prediction trajectory tracking control system and method based on event triggering - Google Patents

Mobile robot model prediction trajectory tracking control system and method based on event triggering Download PDF

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CN113031436A
CN113031436A CN202110212793.3A CN202110212793A CN113031436A CN 113031436 A CN113031436 A CN 113031436A CN 202110212793 A CN202110212793 A CN 202110212793A CN 113031436 A CN113031436 A CN 113031436A
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CN113031436B (en
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贺宁
齐荔鹏
陈烁吉
刘月笙
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Xian University of Architecture and Technology
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Abstract

The invention provides a mobile robot model prediction trajectory tracking control system and method based on event triggering, which comprises the following steps: designing to obtain a model predictive controller; setting the current initial state of the mobile robot, generating a reference track, and obtaining a state prediction value of the mobile robot at the next moment; taking the obtained state prediction value at the next moment as a new current state of the mobile robot; setting an event trigger mechanism, and judging whether the new current state meets a trigger condition; repeating the execution until the last track point on the discretized reference track is tracked; by designing the event trigger mechanism, the model predictive controller only acts at the occurrence moment of the set event, so that compared with the traditional periodic sampling control, the event trigger mechanism only acts at the occurrence moment of the set event, for example, the error exceeds a threshold value or reaches a specific moment, the path following control is realized, and the calculation amount is greatly reduced.

Description

Mobile robot model prediction trajectory tracking control system and method based on event triggering
Technical Field
The invention belongs to the field of intelligence, and particularly relates to a mobile robot model prediction trajectory tracking control system and method based on event triggering.
Background
The tracking control method of the mobile robot generates more research results in recent years, mainstream tracking control algorithms at present comprise synovial control, model predictive control, robust control and the like, and the model predictive control is widely applied to the field of mobile robot control by virtue of the advantages of the model predictive control on system constraint and multi-objective optimization problem processing.
Model predictive control needs to solve a constraint optimization problem at each sampling moment, so that a large demand exists on online calculation amount. Aiming at the problem, a robust predictive control algorithm based on event triggering is provided in the prior art, and it needs to be emphasized that although the event triggering predictive control algorithm can process external disturbance through a terminal cost function, a terminal constraint and a tightening set, the additional addition items can greatly increase the online calculation amount of the optimization problem, seriously affect the real-time performance of the controller and reduce the optimization performance of the controller, and under the condition of limited hardware equipment performance, the problems that the optimization problem cannot be solved in time, control signals cannot be updated in time and the like can exist, so that the system performance is deteriorated and even unstable, and therefore, certain application and popularization difficulties exist.
Disclosure of Invention
The invention aims to provide a mobile robot model prediction trajectory tracking control system and method based on event triggering, and overcomes the defect that the real-time performance of a controller is reduced due to large calculated amount in the conventional model prediction control.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention provides a mobile robot model prediction trajectory tracking control method based on event triggering, which comprises the following steps:
step 1, establishing a linearized discrete model of a mobile robot according to a nonlinear kinematics model of the mobile robot, obtaining a linearized time-varying model according to the linearized discrete model of the mobile robot, taking the linearized time-varying model as a prediction model, and designing according to the prediction model to obtain a model prediction controller;
step 2, setting a current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment when t is equal to k;
step 3, combining the current initial state of the mobile robot, the first track point and the model prediction controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
step 4, updating the current initial state of the mobile robot set in the step 2 by using the first element in the obtained control input increment sequence to obtain a state prediction value of the mobile robot at the next moment;
step 5, taking the obtained state prediction value at the next moment as the new current state of the mobile robot;
step 6, setting an event trigger mechanism, and judging whether the new current state meets a trigger condition, wherein:
if yes, at the moment when t is k +1, the model prediction controller combines the new current position state and the next track point on the discretized reference track to solve and obtain a new control input increment sequence of the mobile robot in the control time domain, updates the current state of the mobile robot by using the first element in the new control input increment sequence to obtain a state prediction value of the mobile robot at the next moment, and enters the step 5;
if not, updating the state predicted value obtained in the step 4 by using the first element of the control input increment sequence obtained at the time t-k +1 to obtain a new state predicted value of the mobile robot at the next time, and entering a step 5;
and 7, repeating the step 5 and the step 6 until the last track point on the discretized reference track is tracked.
Preferably, in step 1, a model predictive controller is obtained according to a nonlinear kinematics model of the mobile robot, and the specific method is as follows:
obtaining a linear discrete model of the mobile robot according to the nonlinear kinematics model of the mobile robot;
obtaining a linear time-varying model according to the obtained linearized discrete model of the mobile robot; and taking the linear time-varying model as a prediction model, and designing according to the prediction model to obtain the model prediction controller.
Preferably, the linearized discrete model of the mobile robot is obtained according to a nonlinear kinematics model of the mobile robot, and the specific method is as follows:
establishing a nonlinear kinematics model of the mobile robot, and performing linearization processing on the nonlinear kinematics model by adopting a Taylor series expansion mode to obtain a linear error model; and discretizing the linear error model by adopting an Euler method to obtain a linearized discrete model of the mobile robot.
Preferably, in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than the pose coordinate of the state component of the threshold curve, setting the following trigger conditions:
Figure BDA0002952971190000031
in the formula, xi1，ξ2ξ 3 denotes the state components x, y,
Figure BDA0002952971190000032
σx，σyand
Figure BDA0002952971190000033
representing the state components x, y,
Figure BDA0002952971190000034
a corresponding threshold value.
Preferably, the threshold curve is obtained by:
in the track tracking process, selecting the pose coordinates of the mobile robot at the same sampling moment from N groups of historical data and averaging the pose coordinates to obtain three variables;
setting the three variables as a threshold value triggered by the event at the first sampling moment;
respectively obtaining state component pose coordinate threshold curves of the three mobile robots according to the obtained thresholds triggered by the events:
Figure BDA0002952971190000035
preferably, in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than the state component pose coordinate of the upper bound of the threshold band or smaller than the state component coordinate of the lower bound of the threshold band, setting the following triggering conditions:
Figure BDA0002952971190000041
in the formula, xi1，ξ2，ξ3Representing the state components x, y,
Figure BDA0002952971190000042
σx_u、σx_d、σy_u、σy_d、
Figure BDA0002952971190000043
and
Figure BDA0002952971190000044
and respectively represent upper and lower threshold values of a horizontal coordinate, a vertical coordinate and a rotation angle.
Preferably, the threshold band is obtained by:
the relationship between the threshold curve and the maximum perturbation is used to form a threshold band:
Figure BDA0002952971190000045
wherein the content of the first and second substances,
Figure BDA0002952971190000046
representing the upper bound of the perturbation.
A mobile robot model prediction trajectory tracking control system based on event triggering can execute the control method and comprises a model building module, a module parameter setting module, a data processing module and a data judging module, wherein:
the model construction module is used for establishing a linearized discrete model of the mobile robot according to the nonlinear kinematics model of the mobile robot, taking the linearized discrete model as a prediction model, and designing according to the prediction model to obtain a model prediction controller;
the module parameter setting module is used for setting the current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment when t is equal to k;
the data processing module is used for combining the current initial state of the mobile robot, the first track point and the model prediction controller and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
updating the current initial state of the set mobile robot by using the first element in the obtained control input increment sequence to obtain a state prediction value of the mobile robot at the next moment;
the data judgment module is used for taking the obtained state prediction value at the next moment as the new current state of the mobile robot; setting an event trigger mechanism, and judging whether the new current state meets a trigger condition, wherein:
if yes, at the moment when t is k +1, the model prediction controller combines the new current position state and the next track point on the discretized reference track to solve and obtain a new control input increment sequence of the mobile robot in the control time domain;
if the current state prediction value is not satisfied, at the time t-k +1, obtaining a new state prediction value of the mobile robot at the next time by using the state prediction value obtained in the first element updating of the control input increment sequence obtained at the time t-k;
and repeating the execution until the last track point on the discretized reference track is tracked.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a mobile robot model prediction track tracking control method based on event triggering, which is characterized in that an event triggering mechanism is designed, so that a model prediction controller only acts at the occurrence moment of a set event, namely for a first triggering strategy, when the pose coordinate of any state component of a mobile robot is larger than the pose coordinate of any state component of a corresponding threshold curve, the model prediction controller considers that a triggering condition is met, the model prediction controller updates and solves a control sequence, otherwise, the first element of the control sequence is continuously applied until the triggering condition is met; for the second trigger strategy, when the pose coordinate of any state component of the mobile robot is larger than the pose coordinate of the state component of the upper bound of the corresponding threshold band or smaller than the pose coordinate of the state component of the lower bound of the threshold band, the model prediction controller is considered to meet the trigger condition, the model prediction controller updates and solves the control sequence, and otherwise, the first element of the control sequence is continuously applied until the trigger condition is met; therefore, compared with the traditional periodic sampling control, the event trigger mechanism only acts at the moment when a given event occurs, such as the error exceeds a threshold value or reaches a specific moment, so that the path following control is realized, and the calculation amount is greatly reduced.
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FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a diagram illustrating the effect of tracking a straight track according to an embodiment;
FIG. 3 is an effect diagram of tracking a circular trajectory according to an embodiment;
FIG. 4 is a graph of the number of times the optimization problem is solved online when two event-triggered strategies track a straight-line trajectory;
FIG. 5 is a graph of the number of times the optimization problem is solved online when two event-triggered strategies trace a circular trajectory.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a mobile robot model prediction trajectory tracking control method based on event triggering, which comprises the following steps:
s1: establishing a nonlinear kinematics model of the mobile robot, and performing linearization processing on the nonlinear kinematics model by adopting a Taylor series expansion mode to obtain a linear error model; discretizing the linear error model by adopting an Euler method to obtain a linearized discrete model of the mobile robot;
s2: obtaining a linear time-varying model according to a linear discrete model of the mobile robot, taking the linear time-varying model as a prediction model, and designing a model prediction controller according to the prediction model; the model predictive controller contains the predictive equations, the control optimization problem that satisfies the objective function and various constraints, and the feedback mechanism.
S3: generating a reference track, and performing discretization processing on the obtained reference track to obtain a discretized reference track; setting an initial state of the mobile robot; selecting a first track point on the discretized reference track at the moment t is equal to k;
s4: combining the first track point, the initial state of the mobile robot and a model prediction controller, bringing a prediction equation into an objective function, solving a control optimization problem meeting the objective function and various constraints, and obtaining a control input increment sequence of the mobile robot in a control time domain
Figure BDA0002952971190000061
S5: inputting the control obtained in S4 into the increment sequence
Figure BDA0002952971190000062
First element of (1)
Figure BDA0002952971190000063
As a control input increment, updating the initial state of the mobile robot by using the control input increment to obtain a state predicted value xi (k +1| k) of the mobile robot at the next moment;
s6: taking the obtained state predicted value xi (k +1| k) as the new current state of the mobile robot;
s7: designing an event trigger mechanism, and judging whether the new current state meets a trigger condition, wherein:
if yes, at the moment when t is k +1, the model prediction controller combines the new current state and the next track point on the discretized reference track to solve the control optimization problem meeting the objective function and various constraints, so as to obtain a new control input increment sequence of the mobile robot in the control time domain, the current state of the mobile robot is updated by using the first element in the new control input increment sequence, a state prediction value of the mobile robot at the next moment is obtained, and the operation enters S6;
if not, the control input increment sequence is not updated at the time t + k +1, the state predicted value obtained in the step S5 is updated by using the first element of the control input increment sequence obtained at the previous time, and the process proceeds to S6;
s8: s6 through S7 are repeatedly performed until the last track point on the discretized reference track is tracked.
In S1, establishing a linearized discrete model of the mobile robot, the specific method is:
s101, establishing a nonlinear kinematics model of the mobile robot, specifically:
assuming that the system accords with incomplete constraint and the vehicle body does not slide laterally, considering that the speed of the robot is generally low and the influence of lateral acceleration such as centrifugal acceleration is small during steering, establishing a kinematic model of the mobile robot as follows:
Figure BDA0002952971190000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002952971190000072
indicating the state of the robot, wherein [ x y]The position is indicated by a position indication,
Figure BDA0002952971190000073
the pose angle of the mobile robot, namely the included angle between the positive direction of the x axis of the mobile robot body coordinate system and the positive direction of the x axis of the global coordinate system, is represented by v and omega respectivelyDegree and angular velocity.
S102, expressing the kinematic model by using a state vector form:
Figure BDA0002952971190000074
Figure BDA0002952971190000075
in the formula, xi is a state vector; u is a control input; f (-) represents the mapping relationship.
S103, the state and the control quantity at any moment of the reference system satisfy the following relation:
Figure BDA0002952971190000081
Figure BDA0002952971190000082
s104, the above formula (3) is arranged at an arbitrary reference point (xi)r,ur) The Taylor series is expanded, only the first-order terms are reserved, and the high-order terms are ignored, so that the following expression can be obtained:
Figure BDA0002952971190000083
s105, the linearized error model of the mobile robot is obtained by subtracting the equations (4) and (3):
Figure BDA0002952971190000084
s106, discretizing the formula (5) by adopting an Euler method to obtain a linear discrete model of the mobile robot:
Figure BDA0002952971190000085
in the formula:
Figure BDA0002952971190000086
in S2, the linear time-varying model designs the predictive controller, and the specific method includes:
s2021, designing a prediction equation:
considering the discretization model equation (6) of the mobile robot, the following are set:
Figure BDA0002952971190000087
a new discrete state space expression can thus be obtained:
Figure BDA0002952971190000091
in the formula
Figure BDA0002952971190000092
Is a matrix of the system, and,
Figure BDA0002952971190000093
is a control matrix that is a function of,
Figure BDA0002952971190000094
is an output matrix, and m and n are respectively dimension of state quantity and control quantity. To simplify the presentation setup:
Figure BDA0002952971190000095
the expression for obtaining the prediction output in the prediction time domain is:
Y(t)＝Ψtμ(k|t)+ΘtΔU(t) (10)
in the formula: :
Figure BDA0002952971190000096
Figure BDA0002952971190000097
in the formula Np，NcRespectively representing the prediction time domain and the control time domain.
S2022, controlling and optimizing:
the target function of the predictive controller comprises information such as system state quantity errors and control quantity changes, and the optimal control problem established based on the target function can ensure that the mobile robot can track the reference track quickly and stably, and the optimal control problem is as follows:
Figure BDA0002952971190000101
s.t.
umin(t+k)≤u(t+k)≤umax(t+k)
Δumin(t+k)≤Δu(t+k)≤Δumax(t+k)
ymin(t+k)≤y(t+k)≤ymax(t+k)
wherein Q and R are weight matrices; n is a radical ofPIs a prediction time domain; n is a radical ofCIs a control time domain; alpha is a weight system; ε is the relaxation factor.
The equation (10) is substituted into the optimization function (11), and the output quantity deviation in the prediction horizon is expressed as:
Figure BDA0002952971190000102
wherein Y isref＝[ηref(t+1|t),...,ηref(t+Np|t)]T
Through the corresponding matrix calculation, the optimization problem can be adjusted to:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t)T,ε]THt[ΔU(t)T,ε]+Gt[ΔU(t)T,ε]+Pt (13)
in the formula:
Figure BDA0002952971190000103
Pt＝E(t)TQE(t)
the constrained optimization solution problem of the model predictive control at each step is equivalent to solving the quadratic programming problem as follows:
Figure BDA0002952971190000104
ΔUmin≤ΔU(k)≤ΔUmax，
Figure BDA0002952971190000105
Ymin-ε≤Ψtμ(k|t)+ΘtΔU(t)≤Ymax-ε,
k＝t,...,t+Nc-1，ε＞0
s2023, after the online solution of the equation (14) is completed at the sampling time in each control period, obtaining a control input increment sequence in the control time domain:
Figure BDA0002952971190000106
the first element in the control sequence is applied to the system as the actual control input increment, namely:
Figure BDA0002952971190000107
and refreshing the optimization problem by using the newly obtained state, and repeating the steps in a circulating way until the control process is finished.
In S6, the event trigger mechanism is designed, including the following steps:
s601, because various disturbances inevitably exist in the actual mobile robot system, the design of the event trigger mechanism needs to further consider the disturbance signal W ∈ W on the basis of the formula (1) and use
Figure BDA0002952971190000111
Represents the upper bound of the perturbation, where W represents the tight set. The state signal taking into account the disturbance is expressed as follows:
Figure BDA0002952971190000112
s602, defining the next trigger time as tk+1The method comprises the following steps:
Figure BDA0002952971190000113
the first triggered trigger strategy design comprises:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than that of the state component of the threshold curve, the MPC controller executes a control action based on which the sequence { t } is definedk|k∈N*Defining the time of the mobile robot for solving the optimization problem by the controller in the path following process
Figure BDA0002952971190000114
For the next trigger moment, the following trigger conditions are set:
Figure BDA0002952971190000115
in the formula, xi1，ξ2，ξ3Representing the state components x, y,
Figure BDA0002952971190000116
σx，σyand
Figure BDA0002952971190000117
representing the state components x, y,
Figure BDA0002952971190000118
corresponding thresholdThe value is obtained.
The selection method of the threshold curve comprises the following steps: selecting the pose coordinates of the mobile robot at the same sampling moment from N groups of historical data, averaging the pose coordinates to obtain three variables, setting the three variables as a threshold triggered by an event at the first sampling moment, wherein a known threshold calculated off-line exists at each sampling moment in the track tracking process, and finally, state component pose coordinate threshold curves of three mobile robots can be respectively obtained:
Figure BDA0002952971190000121
wherein the content of the first and second substances,
Figure BDA0002952971190000122
respectively representing the pose information of the mobile robot in the ith group of sample data, wherein k is the kth sampling moment; sigmax(k)、σy(k)、
Figure BDA0002952971190000123
Respectively representing the threshold values corresponding to the horizontal and vertical coordinates and the rotation angle of the mobile robot at the kth sampling moment.
The second triggered trigger strategy design comprises:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than the state component pose coordinate of the upper bound of the threshold value band or smaller than the state component coordinate of the lower bound of the threshold value band, defining
Figure BDA0002952971190000124
For the next trigger moment, the following trigger conditions are set:
Figure BDA0002952971190000125
in the formula, xi1，ξ2，ξ3Representing the state components x, y,
Figure BDA0002952971190000126
σx_u、σx_d、σy_u、σy_d、
Figure BDA0002952971190000127
and
Figure BDA0002952971190000128
and respectively represent upper and lower threshold values of a horizontal coordinate, a vertical coordinate and a rotation angle.
The selection method of the threshold value band comprises the following steps: under the condition of ensuring that the control effect is not reduced, a threshold value band can be formed by utilizing the relationship between a threshold value curve and the maximum disturbance:
Figure BDA0002952971190000131
in the example, for the straight-line trajectory tracking, the prediction time domain and the control time domain are set to be 5, the control period is 0.05s, and a straight line with y being 10 is set as a reference path.
The error penalty term weight Q ═ 100; 010; 000.5 ], R ═ 0.10; 00.1].
The time trigger is represented by TT, namely the optimization problem is solved at each sampling moment, ET1 and ET2 respectively represent the application of a first event trigger control strategy and a second event trigger control strategy to the controller, and rho is 0.05 to represent the upper bound of the bounded random disturbance.
In the example, for circular trajectory tracking, the prediction time domain and the control time domain are set to 20, the control period is 0.05s, and a circle with a radius of 5m is set as a reference path. The error penalty term weight Q ═ 100; 010; 000.5, [ 0.20; 00.2].
The time trigger is represented by TT, namely the optimization problem is solved at each sampling moment, ET1 and ET2 respectively represent the application of a first event trigger control strategy and a second event trigger control strategy to the controller, and rho is 0.05 to represent the upper bound of the bounded random disturbance.
As can be seen from fig. 4 and 5, on the premise of achieving the tracking effect, after the first and second event-triggered control strategies are introduced, the calculated amount during the linear trajectory tracking is reduced by 26.4% and 74%, and the calculated amount during the circular trajectory tracking is reduced by 18.14% and 75.12%, respectively; meanwhile, the control signal at the last moment is used as the trigger condition is not met, so that the consumption of additional communication resources is reduced.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (8)

1. A mobile robot model prediction trajectory tracking control method based on event triggering is characterized by comprising the following steps:
step 1, establishing a linearized discrete model of a mobile robot according to a nonlinear kinematics model of the mobile robot, obtaining a linearized time-varying model according to the linearized discrete model of the mobile robot, taking the linearized time-varying model as a prediction model, and designing according to the prediction model to obtain a model prediction controller;
step 2, setting an initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment t equal to k;
step 3, combining the initial state of the mobile robot, the first track point and the model prediction controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
step 4, updating the initial state of the mobile robot set in the step 2 by using the first element in the obtained control input increment sequence to obtain a state prediction value of the mobile robot at the next moment;
step 5, taking the obtained state prediction value at the next moment as the new current state of the mobile robot;
step 6, setting an event trigger mechanism, and judging whether the new current state meets a trigger condition, wherein:
if yes, at the moment when t is k +1, the model prediction controller combines the new current position state and the next track point on the discretized reference track to solve and obtain a new control input increment sequence of the mobile robot in the control time domain, updates the current state of the mobile robot by using the first element in the new control input increment sequence to obtain a state prediction value of the mobile robot at the next moment, and enters the step 5;
if not, updating the state predicted value obtained in the step 4 by using the first element of the control input increment sequence obtained at the time t-k +1 to obtain a new state predicted value of the mobile robot at the next time, and entering a step 5;
and 7, repeating the step 5 and the step 6 until the last track point on the discretized reference track is tracked.
2. The event-triggered mobile robot model prediction trajectory tracking control method according to claim 1, wherein in step 1, a model prediction controller is obtained according to a nonlinear kinematics model of the mobile robot, and the specific method is as follows:
obtaining a linear discrete model of the mobile robot according to the nonlinear kinematics model of the mobile robot;
obtaining a linear time-varying model according to the obtained linearized discrete model of the mobile robot; and taking the linear time-varying model as a prediction model, and designing according to the prediction model to obtain the model prediction controller.
3. The event-triggered mobile robot model prediction trajectory tracking control method according to claim 2, wherein a linearized discrete model of the mobile robot is obtained according to a nonlinear kinematics model of the mobile robot, and the specific method is as follows:
establishing a nonlinear kinematics model of the mobile robot, and performing linearization processing on the nonlinear kinematics model by adopting a Taylor series expansion mode to obtain a linear error model; and discretizing the linear error model by adopting an Euler method to obtain a linearized discrete model of the mobile robot.
4. The event-triggered mobile robot model prediction trajectory tracking control method according to claim 1, wherein in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than the pose coordinate of the state component of the threshold curve, setting the following trigger conditions:
Figure FDA0002952971180000021
in the formula, xi1，ξ2，ξ3Representing the state components x, y,
Figure FDA0002952971180000022
σx，σyand
Figure FDA0002952971180000023
representing the state components x, y,
Figure FDA0002952971180000024
a corresponding threshold value.
5. The event-triggered mobile robot model prediction trajectory tracking control method according to claim 4, wherein the threshold curve obtaining method comprises:
in the track tracking process, selecting the pose coordinates of the mobile robot at the same sampling moment from N groups of historical data and averaging the pose coordinates to obtain three variables;
setting the three variables as a threshold value triggered by the event at the first sampling moment;
respectively obtaining state component pose coordinate threshold curves of the three mobile robots according to the obtained thresholds triggered by the events:
Figure FDA0002952971180000031
6. the event-triggered mobile robot model prediction trajectory tracking control method according to claim 1, wherein in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when the pose coordinate of any state component of the mobile robot is larger than the state component pose coordinate of the upper bound of the threshold band or smaller than the state component coordinate of the lower bound of the threshold band, setting the following triggering conditions:
Figure FDA0002952971180000032
in the formula, xi1，ξ2，ξ3Representing the state components x, y,
Figure FDA0002952971180000033
σx_u、σx_d、σy_u、σy_d、
Figure FDA0002952971180000034
and
Figure FDA0002952971180000035
and respectively represent upper and lower threshold values of a horizontal coordinate, a vertical coordinate and a rotation angle.
7. The event-triggered mobile robot model prediction trajectory tracking control method according to claim 6, wherein the threshold band is obtained by:
the relationship between the threshold curve and the maximum perturbation is used to form a threshold band:
Figure FDA0002952971180000041
wherein the content of the first and second substances,
Figure FDA0002952971180000042
representing the upper bound of the perturbation.
8. An event-triggered mobile robot model prediction trajectory tracking control system, which is characterized by being capable of executing the control method of any one of claims 1 to 7, and comprising a model construction module, a module parameter setting module, a data processing module and a data judgment module, wherein:
the model construction module is used for establishing a linearized discrete model of the mobile robot according to the nonlinear kinematics model of the mobile robot, taking the linearized discrete model as a prediction model, and designing according to the prediction model to obtain a model prediction controller;
the module parameter setting module is used for setting the current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment when t is equal to k;
the data processing module is used for combining the current initial state of the mobile robot, the first track point and the model prediction controller and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
updating the current initial state of the set mobile robot by using the first element in the obtained control input increment sequence to obtain a state prediction value of the mobile robot at the next moment;
the data judgment module is used for taking the obtained state prediction value at the next moment as the new current state of the mobile robot; setting an event trigger mechanism, and judging whether the new current state meets a trigger condition, wherein:
if yes, at the moment when t is k +1, the model prediction controller combines the new current position state and the next track point on the discretized reference track to solve and obtain a new control input increment sequence of the mobile robot in the control time domain;
if the current state prediction value is not satisfied, updating the obtained state prediction value by using the first element of the control input increment sequence obtained at the time t-k +1 to obtain a new state prediction value of the mobile robot at the next time;
and repeating the execution until the last track point on the discretized reference track is tracked.
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